1.Researchers have developed a statistical model that predicts whether a company will go bankrupt over the next 12 months. In a test run, for the firms that went bankrupt the model correctly predicted bankruptcy 90% of the time. For the firms which did not go bankrupt the model also correctly predicted non-bankruptcy 80% of the time.Assume that you expect 10% of the firms in your city to go bankrupt over the next 12 months.

a.Suppose that the model predicts bankruptcy for the firm that you own and located in your city. What is the probability that your firm will not go bankrupt within the next 12 months? Show the necessary steps.

b.What is the probability that the model predicts non-bankruptcy for a randomly selected firm in your city? Briefly show how arrived at your answer.

c.What is the probability that the model will predict bankruptcy for a firm in your city and the firm will fail to go bankrupt? Show the necessary work.

d.What is the probability that the model will predict bankruptcy for a firm in your city or the firm will fail to go bankrupt? Show the necessary work.